Saturday, September 27, 2014

Guest blogger from digiblock.com: place value and division

I'm happy to welcome fellow teacher Avery Stern at Digi Block. She has some fall activities and great division tips as you teach your students!

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What’s More American Than Apple Pie and Fair Shares?

In the words of a soft-rock singer “When autumn comes, it doesn’t ask, it just walks in where it left you last,” and autumn, has marched right in with all things pumpkin, apple, knitted, and spooky. It can also be a time for classroom cooking and group activities - so what better time that to start introducing the daunting division unit than through fun, autumnal themed lessons?

One of the things we really like to emphasize here at Digi-Block is the idea of self-discovery. A way of increasing the likelihood of student engagement and excitement is by introducing this lesson without even whispering the D word; Donuts? Dragon-tales? Dasypoedes? Division.

To young students, division can often seem like the no-good-very-bad-fourth brother of math...But I quite like division...and it’s an undeniably necessary skill. So let’s teach that D word in the most useful way possible - real life scenarios.

Dividing the Pie

In this activity students will:

Use the blocks to determine how to make fair shares of a known quantity

Materials: Digi-Block of 1000, or other manipulative ie. pennies, counters, etc. and worksheet

Introduction:You’ve gone apple or pumpkin, or nose picking; let’s use Digi-Blocks to develop a fundamental understanding of “giving everyone a fair share.”

Instruction: Say you have 15 students in a class, and you’ve picked 240 apples - We’ll use Digi-Blocks as our rot-free substitute. How neat and clean! ... Like our hands before we start dolling out ripe produce.

Have your students predict how many apples, (pumpkins, boogers, or blocks), each child will get depending on the amount they collect.

Have your students brainstorm how to equally distribute the goods. They may start by handing each person one at a time. Thats OKAY! Let them tediously work out the problem.

Now have students pack the blocks into tens and hundreds.

Questions to Ask:

Can each student receive a full block of 100?

Can each student receive a block of 10?

How many single blocks will each student receive?

Were there any leftovers?

Did you have to unpack the blocks to fairly distribute them?

Do you think there are times we won’t be able to fairly distribute the apples? (If students are at a point of extended thinking)

ex answer: “When we change the number of apples or we change the number of people.”

Hmmmmmm. Tricky.

Variations:

Try the lesson with each group using different forms of 100. Ex. Loose single blocks, tens blocks, or pre-packed 100 blocks and remainder. Have students discuss what was easier.

Ask: Why was one way easier than the other? ie. the base 10 number system bundles up units so that we don’t have to individually count.

give some groups apples that will equally share out and have others that will leave them with a remainder. Can students find similarities and differences in division problems that leave remainders. Do the problems out with the blocks.

Pumpkin Carving and All that Leftover Gunk:

Introducing the remainder and peaking student curiosity.

In this activity students will:

- Learn about remainders through self-discovery and real-life problem solving.

Instruction:You can begin by breaking your classroom into even groups. Have your students figure out how large the groups should be as a warm-up to your division lesson.

Provide each student with an array mat, blocks, and a series of short word problems. (worksheet attached).

Ex. You are carving pumpkins for all the houses on your street. There are 7 houses and 68 pumpkins. How many pumpkins will each house get?

Lets show this with blocks.

(insert image pumpkins_packed.jpg)

Question to Ask:

“How can we use what we know to come up with an efficient, simple way, of dividing up these pumpkins/blocks?”

Remind students that packing blocks to represent pumpkins is a great place to start, and they should log their thought processes in their math journals. <-- a great way of assessing progress and deep conceptual understanding.

Students may come up with several different ways of answering the problem. Repeated subtraction*, written work, or distributing in even groups on the array mat are all great options.

Questions to ask:

After they divide, if we took all the pumpkins back, how many would we have? How can we show this with a number sentence? What does this teach us about checking your work?

*Using repeated subtraction as a method of elementary division can be a great way to start. It’s important to emphasize that repeated subtraction is the not the same as division even though repeated addition is multiplication. Can your students figure out the reason for this? Sometimes it takes adults a bit of time as well! Repeated subtraction finds the number of equal groups while sharing finds the number IN each equal group.

ex. 25-8-8-8 = 1 not the same as 25/8 BUT 8+8+8 = 24 which IS the same as 8x3

Variations:

Ask your students not only to share their discoveries, but swap technique with another group.

As for the remainder, remind your students that real-life division means there are real-life solutions to what’s leftover.

Challenge Question: What does the remainder represent and why can’t we just make another group out of it?

Even though we often ignore the remainder in a division problem - If they really did have too many pumpkins, what could they do with it?

Give them to a friend who doesn’t live on the block? Use them to decorate their own front porch? Make pancakes and pumpkin seed snacks out of them? Cut them into bits and leave it for the compost?

Peak your students’ interest. Instill curiosity!

Math is everywhere from the World Series to how many table spoons of cinnamon to toss into that delicious vat of hot cider. Maintaining a clear reminder of this is vital to a student’s engagement.

And just to top it all of, follow this lesson up with a real autumn activity like leaf collecting and dividing, pie baking where division and measurements are unavoidably enjoyable, or my personal favorite; predicting how many pieces of Halloween candy they would need to collect to have enough for a few sweet treats every week!

General Tips for when your students are stuck:

Simplify the problem. Focus on identifying patterns rather than getting the answer correct.

See if they can work backwards and find the exact point in the lesson where the challenge becomes too much.

Encourage self-correction by asking questions to help them identify points of error. ie. They make an incomplete group out of the remainder. Can they workout why this isn’t a viable solution?

Put the blocks away and simply talk about potential solutions. Then dive back in, but slowly! Always start with an easily doable problem. This provides a confident start for students.

And most importantly:

Listen to some dance music. Dance to the dance music. Sing to the dance music. Boogie woogie woogie until you just can’t boogie no more.

Wow! Great info Avery! Thanks for being a guest blogger at Kids Math Teacher. If anyone wants to be a guest simply email me at kidsmathteacher@gmail.com with your guest post idea and we'll go from there. Have a great rest of your weekend!

While organizing activities, decide how much time to spend on group activities and when it would be best to do them. If the activity is to be part of a team meeting, plan it for the appropriate spot on the specific meeting agenda.